A power law is a relationship between two quantities whereby a relative change in one quantity causes a proportional relative change in the other. These relationships are ubiquitous in science and engineering applications, such as the inverse-square law of Newtonian gravity. Power laws are expressed mathematically as equalities of the form y = ax^k. We can determine whether data likely follows a power law by plotting a function through the data and examining the fit. For this problem, we will genereate synthetic data that roughly follows a power law, then demonstrate that the data obeys a power law. Generate data according to a power law at 20 evenly space points on the interval [1.1 10]. Then, or each of our points, add random noise of up to 20% of that point's value. This simulates having noisy data. Next, plot the noisy data using a semilog plot. (Recall matplotlibl) Finally, plot the same power law as before, without noise, at many more points (on the order of 1000) on the same semilog axes as the data. This simulates fitting the data, which we will learn how to do later in the semester. Because of the way we generated the data, the power law should be a good fit for the noisy data. In a real application, this would tell us that the process generating the data likely obeyed a power law